Feature　selection　is　an　important　research　topic　in　machine　learning　and　computer　vision　in　that　it　can　reduce　the　dimensionality　of　input　data　and　improve　the　performance　of　learning　algorithms.　Low-rank　approximation　techniques　can　well　exploit　the　low-rank　property　of　input　data,　which　coincides　with　the　internal　consistency　of　dimensionality　reduction.　In　this　paper,　we　propose　an　efficient　unsupervised　feature　selection　algorithm,　which　incorporates　low-rank　approximation　as　well　as　structure　learning.　First,　using　the　self-representation　of　data　matrix,　we　formalize　the　feature　selection　problem　as　a　matrix　factorization　with　low-rank　constraints.　This　matrix　factorization　formulation　also　embeds　structure　learning　regularization　as　well　as　a　sparse　regularized　term.　Second,　we　present　an　effective　technique　to　approximate　low-rank　constraints　and　propose　a　convergent　algorithm　in　a　batch　mode.　This　technique　can　serve　as　an　algorithmic　framework　for　general　low-rank　recovery　problems　as　well.　Finally,　the　proposed　algorithm　is　validated　in　twelve　publicly　available　datasets　from　machine　learning　repository.　Extensive　experimental　results　demonstrate　that　the　proposed　method　is　capable　to　achieve　competitive　performance　compared　to　existing　state-of-the-art　feature　selection　methods　in　terms　of　clustering　performance.　(C)　2017　Elsevier　B.V.　All　rights　reserved.